Fundamental group of Galois covers of degree 5 surfaces

Abstract

Let $X$ be an algebraic surface of degree $5$, which is considered as a branch cover of $\mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_5$. In this paper, we deal with the fundamental groups of Galois covers of degree $5$ surfaces that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line.